Question

Simplify the following quotient of complex numbers into the form a + bi. (-8-8i)/(1+2i) please explain I do not get this at all

Answer 1

first you need to know that when you multiply a complex number
\[a+bi\] by its complex conjugate \[a-bi\] you get a real number
\[a^2+b^2\]
so that when you multiply
\[1+2i\] by
\[1-2i\] you get
\[1^2+2^2=5\]

Answer 2

then to rewrite this in standard form (i.e. divide) you write
\[\frac{-8-8i}{1+2i}\times \frac{1-2i}{1-2i}\] and this will give a real denominator, so all the work is multiplying out in the numerator

Answer 3

\[\frac{-8-8i}{1+2i}\times \frac{1-2i}{1-2i}=\frac{-24+8i}{5}\]
\[=-\frac{24}{5}+\frac{8}{5}i\]

Answer 4

Thank you